76.5.23 problem 24

Internal problem ID [17443]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 10:37:45 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3 x-y \right ) x^{\prime }+9 y -2 x&=0 \end{align*}

✓ Solution by Maple

Time used: 1.229 (sec). Leaf size: 53

dsolve((3*x(y)-y)*diff(x(y),y)+(9*y-2*x(y))=0,x(y), singsol=all)
 

\[ x \left (y \right ) = \frac {y \left (\sqrt {11}\, \tan \left (\operatorname {RootOf}\left (3 \sqrt {11}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} y^{2}\right )+3 \sqrt {11}\, \ln \left (11\right )-6 \sqrt {11}\, \ln \left (2\right )+6 \sqrt {11}\, c_{1} +2 \textit {\_Z} \right )\right )+1\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 42

DSolve[(3*x[y]-y)*D[x[y],y]+(9*y-2*x[y])==0,x[y],y,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {x(y)}{y}}\frac {3 K[1]-1}{K[1]^2-K[1]+3}dK[1]=-3 \log (y)+c_1,x(y)\right ] \]